The work can be divided into two subjects. The first is concerned with a general formalism for the calculation of small-signal admittance (or impedance) of membranes associated with the opening and closing kinetics of membrane channels. The differences in the admittance function between equilibrium and nonequilibrium channels are studied. Experimental data indicate that the potassium channels of squid axons may be in a nonequilibrium state. The second topic is concerned with the study of "transport noise" associated with the translocation of individual ions within a channel. The movement of an ion may be described as a series of jumps over activation energy barriers and each jump contributes a single current pulse to the total external current. The investigation of transport noise could yield information on the rates of single ion transport steps within the channel.